As pedestrians stood close by the armed men, he went on: "We swear by almighty Allah we will never stop fighting you," according to footage obtained by ITV News.

The Independent understands the dead soldier – who was wearing a Help for Heroes T-shirt – was a member of the Royal Regiment of Fusiliers, which is currently based overseas. He was ambushed by the men as he left the base in Woolwich, south-east London, who attacked him and then dragged his body into the middle of the road to pose for photographs while standing over him waving a cleaver and a gun, according to witnesses.

Mr Cameron was cutting short a meeting with European leaders to chair a meeting of the emergency committee Cobra today as police and security services investigate whether the two men – later shot and wounded by police – were working alone or as part of a bigger group.

"It's the most appalling crime," he told reporters in Paris. "We are obviously urgently seeking the full facts but there are strong indications that it's a terrorist incident."

He said that they were looking at every aspect of security for troops across Britain, but he added: "The best way to defeat terrorism is to make sure you continue to live your life and make sure that terrorism never wins."

The London Mayor Boris Johnson added: "This afternoon's attack in Woolwich is a sickening, deluded and unforgivable act of violence."

Only hours after the attack was carried out, video footage of one of the suspected killers emerged. With his hands bloodied and carrying a cleaver, he is seen telling the bystander with a camera: "I apologise that women had to witness this today but in our lands our women have to see the same. You people will never be safe. Remove your governments – they don't care about you."

The man, who spoke English without a foreign accent, then saunters back across the road towards his victim lying in the street to join his apparent accomplice. The two men made no attempt to escape and charged a police car carrying an armed response team when it arrived at the scene about 15 minutes after the killing, according to a witness.

"The black guy ran at them with a meat cleaver before it stopped and he was right by the car when they shot him," said Julia Wilders, 51, who lives close by. The second man, who had a gun, was also shot, she said.

The men were taken to separate hospitals by air ambulance and they were expected to survive despite their injuries, according to police last night.

The men were believed to have waited outside the Woolwich barracks of the 2nd Battalion, the Princess of Wales's Royal Regiment, which has deployed to Afghanistan and Iraq, where one of its members, Sergeant Johnson Beharry, won the VC.

Military sources said the soldier had left the barracks by car, but witnesses indicated that he was rammed while walking along the road in an apparently pre-arranged ambush, before being attacked while he was propped up against a wall of a block of flats.

One witness, identified only as James, said he and his partner saw two black men attack a young man aged about 20 with kitchen knives like he was "a piece of meat".

"They were hacking at this poor guy, literally," he told LBC Radio, adding that a group of brave women tried to shield the soldier from the two men.

"They were hacking at him, chopping him, cutting him. These two guys were crazed. They were just animals. They dragged him from the pavement and dumped his body in the middle of the road and left his body there."

Children returning from a school trip were kept locked inside nearby Mulgrave Primary School while the police operation played out.

One local woman said she thought she saw one of the suspects preaching in Woolwich town centre about a week ago. Her daughter, Rebecca France, 18, said yesterday: "It was really political and angry. She said she thought it was strange because he was different from the usual guys who preach in the name of Jesus – he wasn't doing that."

The Muslim Council of Britain said the use of "Islamic slogans" indicated they were motivated by their faith. A statement from the council said: "This is a truly barbaric act that has no basis in Islam and we condemn this unreservedly. Our thoughts are with the victim and his family. We understand the victim is a serving member of the armed forces. Muslims have long served in this country's armed forces, proudly and with honour.

"This attack on a member of the armed forces is dishonourable, and no cause justifies this murder."

Police had set up a series of cordons around the scene last night with extra police patrols in the area and helicopters crossing the skies overhead. The Independent Police Complaints Commission said it sent 12 investigators to the scene to investigate the police shooting after reports of at least six shots being fired.

Shortly before 10pm last night the Metropolitan Police Commissioner, Sir Bernard Hogan-Howe, confirmed the murder investigation was being led by Counter Terrorism Command with two men arrested. He added: “It is hard to comprehend the shocking and horrific scenes we have seen this afternoon on a busy street as Londoners went about their day as normal.”

Last night there were clashes between EDL supporters and police in Woolwich after officers surrounded the local Islamic centre.

Islamists have threatened a number of times to behead a British soldier in retaliation for involvement in wars in Afghanistan and Iraq. Six years ago a group of British Pakistanis based in Birmingham were convicted of plotting such an attack and their leader, Parviz Khan, received a life sentence.

Khan admitted planning to lure a soldier off the streets then film the beheading. He was described in court as having the "most violent and extreme Islamist views" and his aim was to deter any Muslim from joining the British Army.

'Bring back monitoring bill' calls

The brutal terrorist killing of a man on the streets of London sparked calls for the Government to revive plans to extend internet and email monitoring powers to the security services.

Former independent reviewer of terror laws Lord Carlile said it should provoke a "pause for thought" on the decision to drop the planned Communcations Data Bill from the Queen's Speech.

And Labour ex-home secretary Lord Reid said such measures were "essential" to combating terrorism, warning it could otherwise take "some huge tragedy" to show the decision was wrong.

Full-scale legislation was dropped from last month's Queen's Speech in the face of Liberal Democrat opposition to what critics dubbed a "snooper's charter".

Prime Minister David Cameron had warned scrapping the plans would put national security at risk by making it harder to bring terror suspects and other criminals to justice.

But Deputy Prime Minister Nick Clegg blocked the change, insisting the wide-ranging proposals would create a "treasure trove of data" that was neither workable nor proportionate.

Ministers are now in talks with internet firms over alternative law changes.

Speaking on BBC2's Newsnight, Lord Carlile said: "We have to learn proportionate lessons from what has occurred.

"We mustn't rush to judgment. But we must ensure that the police and the security services have for the future the tools they need which wil enable them to prevent this kind of attack taking place.

"I hope that this will give the Government pause for thought about their abandonment for example of the Communcations Data Bill and possibly pause for thought about converting control orders into what are now called Tpims, with a diluted set of powers.

"Lone wolves, even though they are always inevitably connected at least with internet training, are very difficult to catch so we must give the authorities proportionate tools to catch them."

He said he was "not suggesting they had anything to do with today's attack".

"But I am suggesting that the powers that existed in the past but I am suggesting that the powers that existed in the past make it more likely that other events can be prevented in the future," he said.

"This may be a small example of something much bigger which could happen. We must ensure the laws are fit for purpose."

Lord Reid said mobile phone data had been crucial in foiling the 2006 plot to blow up airliners using liquid explosives but that terrorists now used online communication.

"Had we not had that method of connecting people through their communications, 2,500 people would probably have been blown out of the sky over the United Kingdom. It was a vital component.

"But now people have moved on from mobile phones to internet, email, text, Skype. We don't have the means of doing what we did six years ago.

"That is where some of the measures the Government has refused to implement, like data communication, is absolutely essential for effective fighting of terrorism. "You will never find out whether you are right on this one until there is some huge tragedy that might have been averted if they had updated the communication appraisals that can be carried out at GCHQ."